The prebuilt is straight out. You never get a good deal.
The build you put together yourself isn't looking so good either. The i7-860 is NOT a good gaming CPU. Heck, most people don't even consider an option for any build. The 5770 is a weak gaming GPU, especially since you only have 1 PCIe 2.0 slot at a decent speed.
Given your budget (about $1,000 US for the tower, $200 for the monitor, $100 for the OS), I would build something like this (I'll take a look on availability at ebuyer):
CPU: X3 435 60
Mobo: Gigabyte GA-790XTA-UD4 102
RAM: G.Skill Ripjaws 2x2 GB 1600 mhz CAS Latency 7 110
GPU: HD 5870 312
HDD: Seagate 7200.12 500 GB 38. This is a little faster in gaming over the Samsung, but they're basicaly interchangeable
PSU: Corsair 750W 95
Case: HAF 922 83
Optical: Cheap SATA DVD burner 10
Total: 816. If that's a little too expensive, drop the 5870 to a 5850.
With speakers some of the reviews for the cheaper 2.1 ones say the bass is too much.. and i really don't want to spend a lot on them. Like under £50.
You could either get a cheap keyboard and mouse and then just get a good set of speakers and then just save up to get yourself a good keyboard and mouse. Or you could get a cheap set of speakers and get a good keyboard and mouse and just save up to get a good set of speakers.